Question

How do you find $\underset{x\to 0}{lim}\frac{\cos x}{x}$?

Answer 1

Solve using the rules of limit evaluation

The given expression is $\underset{x\to 0}{lim}\frac{\cos x}{x}$.

Here, we know that,

As $x\to 0$, $\cos x\to 1$ $\mathrm{[}\mathrm{\because }\mathrm{}\cos \mathrm{0}\mathrm{°}\mathrm{}\mathrm{=}\mathrm{}\mathrm{1}\mathrm{]}$

Therefore, $\underset{x\to 0}{lim}\frac{\cos x}{x}=\frac{1}{0}$

$\mathrm{\because }$ The value of $\frac{n}{0}$ is undefined, where $n$ is any number.

$\therefore$ $\underset{x\to 0}{lim}\frac{\cos x}{x}=$undefined

Hence, the value of $\underset{x\to 0}{lim}\frac{\cos x}{x}$ is undefined.